"""simple docstring"""







from __future__ import annotations



def      lowercase__(			__SCREAMING_SNAKE_CASE				:	list[int]	,     __SCREAMING_SNAKE_CASE				:	list[int]	,     __SCREAMING_SNAKE_CASE				:	list[int]	,     __SCREAMING_SNAKE_CASE				:	list[list[str]]	,     __SCREAMING_SNAKE_CASE				:	int	,     ):
     lowercase_      :							Optional[int]						=      len(__SCREAMING_SNAKE_CASE )

     # If row is equal to the size of the board it means there are a queen in each row in
     # the current board (possible_board)
     if row == n:
          # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
          # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
          boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board] )
          return

     # We iterate each column in the row to find all possible results in each row
     for col in range(__SCREAMING_SNAKE_CASE ):
          # We apply that we learned previously. First we check that in the current board
          # (possible_board) there are not other same value because if there is it means
          # that there are a collision in vertical. Then we apply the two formulas we
          # learned before:
          #
          # 45º: y - x = b or 45: row - col = b
          # 135º: y + x = b or row + col = b.
          #
          # And we verify if the results of this two formulas not exist in their variables
          # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
          #
          # If any or these are True it means there is a collision so we continue to the
          # next value in the for loop.
          if (
              col in possible_board
              or row - col in diagonal_right_collisions
              or row + col in diagonal_left_collisions
          ):
               continue

          # If it is False we call dfs function again and we update the inputs
          depth_first_search(
              [*possible_board, col]	,     [*diagonal_right_collisions, row - col]	,     [*diagonal_left_collisions, row + col]	,     __SCREAMING_SNAKE_CASE	,     __SCREAMING_SNAKE_CASE	,     )



def      lowercase__(			__SCREAMING_SNAKE_CASE				:	int ):
     lowercase_      :							list[list[str]]						=      []
     depth_first_search([]	,     []	,     []	,     __SCREAMING_SNAKE_CASE	,     __SCREAMING_SNAKE_CASE )

     # Print all the boards
     for board in boards:
          for column in board:
               print(__SCREAMING_SNAKE_CASE )
          print('' )

     print(len(__SCREAMING_SNAKE_CASE )	,     'solutions were found.' )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       n_queens_solution(4)






'''simple docstring'''



def        UpperCAmelCase (    A	:					int					):
							if not isinstance(A       ,		A					):
														SCREAMING_SNAKE_CASE       :   List[str]         =      F"""Input value of [number={number}] must be an integer"""
														raise TypeError(A					)
							if number < 0:
														return False
							SCREAMING_SNAKE_CASE       :   List[str]         =      number * number
							while number > 0:
														if number % 10 != number_square % 10:
																					return False
														number //= 10
														number_square //= 10
							return True


if __name__ == "__main__":
							import doctest

							doctest.testmod()




